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Unformatted text preview: DC Circuit Theorems Superposition 3 Superposition In this lecture, you will: Learn the principle of superposition Learn how to apply the principle of superposition to solve DC circuits Understand the tradeoffs in applying superposition versus other circuit analysis approaches 4 Linearity Linear operators: Add and subtract Multiply and divide by constants Differentiate and integrate Nonlinear operators: Exponents other than 1 For example, squares and square roots Logarithms and many other functions. 5 Linear Circuit Elements Resistors are linear circuit elements: V = IR is clearly a straight line. Ideal capacitors and inductors are linear. Independent sources are linear. Dependent sources are linear provided that the output voltage or current is proportional to the first power of a specified voltage or current (or a sum of these). 6 Nonlinear Circuit Elements Semiconductor devices are nonlinear. Diodes Transistors Devices using ferromagnetic materials are nonlinear. Iron core inductors. Many other real world devices are nonlinear although their response may be approximately linear over a limited range. 7 Linear Circuits A linear circuit is a circuit composed exclusively of linear circuit elements. 3 A 5 10 40 + 50 V-8 Superposition Superposition is a property of all linear systems: [ ] [ ] ) ( ) ( ) ( y f b x f a by ax f + = + 9 Superposition Definition : Any linear system obeys the principle of superposition , which states that whenever a linear system is excited or driven by more than one independent source of energy, the total response is the sum of the individual responses that result from each independent source acting alone. 10 What does this mean? Since we are dealing with linear circuits, we can determine the response of the circuit to each independent source acting alone and then sum the results. Of course, superposition only makes sense when there is more than one independent source. 11 Superposition Example IR V = 2A-+ V R 3A 10 ( 29 ( 29 ( 29 ( 29 ( 29 V A V A V Total V V A V V A V R R R R R . 10 30 20 3 2 . 30 10 3 3 . 20 10 2 2-=-= + =-= -= = = 12 Superposition in Circuits The response in a linear circuit having more than one independent source can be obtained by adding the responses caused by the separate independent sources acting alone. How do I find the response of the circuit to one source acting alone? Turn off all of the other sources. 13 Turned Off Voltage Source Voltage source always provides the specified voltage between its terminals. Current determined by the attached circuit. Turned off means V S = 0 volts Behaves like a short circuit. +-V S a b I I V V S S Short Circuit a b 14 Turned Off Current Source Current source always provides the specified current....
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